Elliptic curve isogeny class with Cremona label 139230f (LMFDB label 139230.eh)

• Label: 139230f
• Number of curves: $4$
• Conductor: $139230$
• CM: no
• Rank: $1$

Elliptic curves in class 139230f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
139230.eh4	139230f1	\([1, -1, 1, -127832, 14056539]\)	\(316892346232279609/66830400000000\)	\(48719361600000000\)	\([2]\)	\(1474560\)	\(1.9167\)	\(\Gamma_0(N)\)-optimal
139230.eh2	139230f2	\([1, -1, 1, -1927832, 1030696539]\)	\(1086934883783829079609/69785974440000\)	\(50873975366760000\)	\([2, 2]\)	\(2949120\)	\(2.2633\)
139230.eh1	139230f3	\([1, -1, 1, -30844832, 65943578139]\)	\(4451879473171293653671609/18353298600\)	\(13379554679400\)	\([2]\)	\(5898240\)	\(2.6099\)
139230.eh3	139230f4	\([1, -1, 1, -1810832, 1161174939]\)	\(-900804278922017287609/277087063526418600\)	\(-201996469310759159400\)	\([2]\)	\(5898240\)	\(2.6099\)

Rank

The elliptic curves in class 139230f have rank \(1\).

Complex multiplication

The elliptic curves in class 139230f do not have complex multiplication.

Modular form 139230.2.a.f

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.